# Averaging method for differential equations perturbed by dynamical systems

ESAIM: Probability and Statistics (2002)

- Volume: 6, page 33-88
- ISSN: 1292-8100

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topPène, Françoise. "Averaging method for differential equations perturbed by dynamical systems." ESAIM: Probability and Statistics 6 (2002): 33-88. <http://eudml.org/doc/245789>.

@article{Pène2002,

abstract = {In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption of multiple decorrelation in terms of this dynamical system. We show how this property can be verified for ergodic algebraic toral automorphisms and point out the fact that, for two-dimensional dispersive billiards, it is a consequence of the method developed in [18]. Moreover, the singular case of a degenerated limit distribution is also considered.},

author = {Pène, Françoise},

journal = {ESAIM: Probability and Statistics},

keywords = {dynamical system; hyperbolicity; billiard; suspension flow; limit theorem; averaging method; perturbation; differential equation; exponential decay of correlations; toral automorphism; Sinai billiards},

language = {eng},

pages = {33-88},

publisher = {EDP-Sciences},

title = {Averaging method for differential equations perturbed by dynamical systems},

url = {http://eudml.org/doc/245789},

volume = {6},

year = {2002},

}

TY - JOUR

AU - Pène, Françoise

TI - Averaging method for differential equations perturbed by dynamical systems

JO - ESAIM: Probability and Statistics

PY - 2002

PB - EDP-Sciences

VL - 6

SP - 33

EP - 88

AB - In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption of multiple decorrelation in terms of this dynamical system. We show how this property can be verified for ergodic algebraic toral automorphisms and point out the fact that, for two-dimensional dispersive billiards, it is a consequence of the method developed in [18]. Moreover, the singular case of a degenerated limit distribution is also considered.

LA - eng

KW - dynamical system; hyperbolicity; billiard; suspension flow; limit theorem; averaging method; perturbation; differential equation; exponential decay of correlations; toral automorphism; Sinai billiards

UR - http://eudml.org/doc/245789

ER -

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